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Chords of harry

Edit 0 3 …
Below are listed the dyadic chords of 11-limit harry temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismicmic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove.

The normal mapping for harry is har = [<2 4 7 7 9|, <0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = <2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.

Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. There is essentially no advantage in accuracy to optimizing for jove temperament rather than harry; in addition to what jove tempers out, harry tempers out 4000/3993. However, POTE tuning, for example, shrinks the three cents of this comma to -0.0827 cents, which is hardly worth worrying about. Hence harry is one way of exploring and organizing the chords of jove, which are therefore also listed below.

Triads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-201-401
 1-9/7-7/6
 swetismic
 8
2
 0-202-401
 1-20/11-7/6
 swetismic
 8
3
 0-202-501
 1-20/11-10/9
 utonal
 10
4
 0-301-501
 1-11/9-10/9
 otonal
 10
5
 0-201-502
 1-9/7-11/7
 otonal
 10
6
 0-301-502
 1-11/9-11/7
 utonal
 10
7
 0-201-602
 1-9/7-3/2
 utonal
 12
8
 0-301-602
 1-11/9-3/2
 rastmic
 12
9
 0-401-602
 1-7/6-3/2
 otonal
 12
10
 0-201-702
 1-9/7-10/7
 otonal
 14
11
 0-202-702
 1-20/11-10/7
 utonal
 14
12
 0-301-702
 1-11/9-10/7
 swetismic
 14
13
 0-401-702
 1-7/6-10/7
 swetismic
 14
14
 0-501-702
 1-10/9-10/7
 utonal
 14
15
 0-502-702
 1-11/7-10/7
 otonal
 14
16
 0-201-903
 1-9/7-11/6
 swetismic
 18
17
 0-301-903
 1-11/9-11/6
 utonal
 18
18
 0-401-903
 1-7/6-11/6
 otonal
 18
19
 0-502-903
 1-11/7-11/6
 utonal
 18
20
 0-602-903
 1-3/2-11/6
 otonal
 18
21
 0-702-903
 1-10/7-11/6
 swetismic
 18
22
 0-301-1003
 1-11/9-7/4
 werckismic
 20
23
 0-401-1003
 1-7/6-7/4
 utonal
 20
24
 0-501-1003
 1-10/9-7/4
 werckismic
 20
25
 0-502-1003
 1-11/7-7/4
 werckismic
 20
26
 0-602-1003
 1-3/2-7/4
 otonal
 20
27
 0-702-1003
 1-10/7-7/4
 werckismic
 20
28
 0-202-1103
 1-20/11-5/3
 utonal
 22
29
 0-401-1103
 1-7/6-5/3
 otonal
 22
30
 0-501-1103
 1-10/9-5/3
 utonal
 22
31
 0-602-1103
 1-3/2-5/3
 otonal
 22
32
 0-702-1103
 1-10/7-5/3
 utonal
 22
33
 0-903-1103
 1-11/6-5/3
 otonal
 22
34
 0-201-1202
 1-9/7-9/8
 utonal
 24
35
 0-301-1202
 1-11/9-9/8
 rastmic
 24
36
 0-502-1202
 1-11/7-9/8
 werckismic
 24
37
 0-602-1202
 1-3/2-9/8
 ambitonal
 24
38
 0-702-1202
 1-10/7-9/8
 werckismic
 24
39
 0-903-1202
 1-11/6-9/8
 rastmic
 24
40
 0-1003-1202
 1-7/4-9/8
 otonal
 24
41
 0-301-1503
 1-11/9-11/8
 utonal
 30
42
 0-502-1503
 1-11/7-11/8
 utonal
 30
43
 0-602-1503
 1-3/2-11/8
 otonal
 30
44
 0-903-1503
 1-11/6-11/8
 utonal
 30
45
 0-1003-1503
 1-7/4-11/8
 otonal
 30
46
 0-1202-1503
 1-9/8-11/8
 otonal
 30
47
 0-202-1703
 1-20/11-5/4
 utonal
 34
48
 0-501-1703
 1-10/9-5/4
 utonal
 34
49
 0-602-1703
 1-3/2-5/4
 otonal
 34
50
 0-702-1703
 1-10/7-5/4
 utonal
 34
51
 0-1003-1703
 1-7/4-5/4
 otonal
 34
52
 0-1103-1703
 1-5/3-5/4
 utonal
 34
53
 0-1202-1703
 1-9/8-5/4
 otonal
 34
54
 0-1503-1703
 1-11/8-5/4
 otonal
 34

Tetrads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-201-401-602
 1-9/7-7/6-3/2
 swetismic
 12
2
 0-201-401-702
 1-9/7-7/6-10/7
 swetismic
 14
3
 0-202-401-702
 1-20/11-7/6-10/7
 swetismic
 14
4
 0-202-501-702
 1-20/11-10/9-10/7
 utonal
 14
5
 0-301-501-702
 1-11/9-10/9-10/7
 swetismic
 14
6
 0-201-502-702
 1-9/7-11/7-10/7
 otonal
 14
7
 0-301-502-702
 1-11/9-11/7-10/7
 swetismic
 14
8
 0-201-401-903
 1-9/7-7/6-11/6
 swetismic
 18
9
 0-201-502-903
 1-9/7-11/7-11/6
 swetismic
 18
10
 0-301-502-903
 1-11/9-11/7-11/6
 utonal
 18
11
 0-201-602-903
 1-9/7-3/2-11/6
 swetismic
 18
12
 0-301-602-903
 1-11/9-3/2-11/6
 rastmic
 18
13
 0-401-602-903
 1-7/6-3/2-11/6
 otonal
 18
14
 0-201-702-903
 1-9/7-10/7-11/6
 swetismic
 18
15
 0-301-702-903
 1-11/9-10/7-11/6
 swetismic
 18
16
 0-401-702-903
 1-7/6-10/7-11/6
 swetismic
 18
17
 0-502-702-903
 1-11/7-10/7-11/6
 swetismic
 18
18
 0-301-501-1003
 1-11/9-10/9-7/4
 werckismic
 20
19
 0-301-502-1003
 1-11/9-11/7-7/4
 werckismic
 20
20
 0-301-602-1003
 1-11/9-3/2-7/4
 jove
 20
21
 0-401-602-1003
 1-7/6-3/2-7/4
 ambitonal
 20
22
 0-301-702-1003
 1-11/9-10/7-7/4
 jove
 20
23
 0-401-702-1003
 1-7/6-10/7-7/4
 jove
 20
24
 0-501-702-1003
 1-10/9-10/7-7/4
 werckismic
 20
25
 0-502-702-1003
 1-11/7-10/7-7/4
 werckismic
 20
26
 0-202-401-1103
 1-20/11-7/6-5/3
 swetismic
 22
27
 0-202-501-1103
 1-20/11-10/9-5/3
 utonal
 22
28
 0-401-602-1103
 1-7/6-3/2-5/3
 otonal
 22
29
 0-202-702-1103
 1-20/11-10/7-5/3
 utonal
 22
30
 0-401-702-1103
 1-7/6-10/7-5/3
 swetismic
 22
31
 0-501-702-1103
 1-10/9-10/7-5/3
 utonal
 22
32
 0-401-903-1103
 1-7/6-11/6-5/3
 otonal
 22
33
 0-602-903-1103
 1-3/2-11/6-5/3
 otonal
 22
34
 0-702-903-1103
 1-10/7-11/6-5/3
 swetismic
 22
35
 0-201-502-1202
 1-9/7-11/7-9/8
 werckismic
 24
36
 0-301-502-1202
 1-11/9-11/7-9/8
 jove
 24
37
 0-201-602-1202
 1-9/7-3/2-9/8
 utonal
 24
38
 0-301-602-1202
 1-11/9-3/2-9/8
 rastmic
 24
39
 0-201-702-1202
 1-9/7-10/7-9/8
 werckismic
 24
40
 0-301-702-1202
 1-11/9-10/7-9/8
 jove
 24
41
 0-502-702-1202
 1-11/7-10/7-9/8
 werckismic
 24
42
 0-201-903-1202
 1-9/7-11/6-9/8
 jove
 24
43
 0-301-903-1202
 1-11/9-11/6-9/8
 rastmic
 24
44
 0-502-903-1202
 1-11/7-11/6-9/8
 jove
 24
45
 0-602-903-1202
 1-3/2-11/6-9/8
 rastmic
 24
46
 0-702-903-1202
 1-10/7-11/6-9/8
 jove
 24
47
 0-301-1003-1202
 1-11/9-7/4-9/8
 jove
 24
48
 0-502-1003-1202
 1-11/7-7/4-9/8
 werckismic
 24
49
 0-602-1003-1202
 1-3/2-7/4-9/8
 otonal
 24
50
 0-702-1003-1202
 1-10/7-7/4-9/8
 werckismic
 24
51
 0-301-502-1503
 1-11/9-11/7-11/8
 utonal
 30
52
 0-301-602-1503
 1-11/9-3/2-11/8
 rastmic
 30
53
 0-301-903-1503
 1-11/9-11/6-11/8
 utonal
 30
54
 0-502-903-1503
 1-11/7-11/6-11/8
 utonal
 30
55
 0-602-903-1503
 1-3/2-11/6-11/8
 ambitonal
 30
56
 0-301-1003-1503
 1-11/9-7/4-11/8
 werckismic
 30
57
 0-502-1003-1503
 1-11/7-7/4-11/8
 werckismic
 30
58
 0-602-1003-1503
 1-3/2-7/4-11/8
 otonal
 30
59
 0-301-1202-1503
 1-11/9-9/8-11/8
 rastmic
 30
60
 0-502-1202-1503
 1-11/7-9/8-11/8
 werckismic
 30
61
 0-602-1202-1503
 1-3/2-9/8-11/8
 otonal
 30
62
 0-903-1202-1503
 1-11/6-9/8-11/8
 rastmic
 30
63
 0-1003-1202-1503
 1-7/4-9/8-11/8
 otonal
 30
64
 0-202-501-1703
 1-20/11-10/9-5/4
 utonal
 34
65
 0-202-702-1703
 1-20/11-10/7-5/4
 utonal
 34
66
 0-501-702-1703
 1-10/9-10/7-5/4
 utonal
 34
67
 0-501-1003-1703
 1-10/9-7/4-5/4
 werckismic
 34
68
 0-602-1003-1703
 1-3/2-7/4-5/4
 otonal
 34
69
 0-702-1003-1703
 1-10/7-7/4-5/4
 werckismic
 34
70
 0-202-1103-1703
 1-20/11-5/3-5/4
 utonal
 34
71
 0-501-1103-1703
 1-10/9-5/3-5/4
 utonal
 34
72
 0-602-1103-1703
 1-3/2-5/3-5/4
 ambitonal
 34
73
 0-702-1103-1703
 1-10/7-5/3-5/4
 utonal
 34
74
 0-602-1202-1703
 1-3/2-9/8-5/4
 otonal
 34
75
 0-702-1202-1703
 1-10/7-9/8-5/4
 werckismic
 34
76
 0-1003-1202-1703
 1-7/4-9/8-5/4
 otonal
 34
77
 0-602-1503-1703
 1-3/2-11/8-5/4
 otonal
 34
78
 0-1003-1503-1703
 1-7/4-11/8-5/4
 otonal
 34
79
 0-1202-1503-1703
 1-9/8-11/8-5/4
 otonal
 34

Pentads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-201-401-602-903
 1-9/7-7/6-3/2-11/6
 swetismic
 18
2
 0-201-401-702-903
 1-9/7-7/6-10/7-11/6
 swetismic
 18
3
 0-201-502-702-903
 1-9/7-11/7-10/7-11/6
 swetismic
 18
4
 0-301-502-702-903
 1-11/9-11/7-10/7-11/6
 swetismic
 18
5
 0-301-501-702-1003
 1-11/9-10/9-10/7-7/4
 jove
 20
6
 0-301-502-702-1003
 1-11/9-11/7-10/7-7/4
 jove
 20
7
 0-202-401-702-1103
 1-20/11-7/6-10/7-5/3
 swetismic
 22
8
 0-202-501-702-1103
 1-20/11-10/9-10/7-5/3
 utonal
 22
9
 0-401-602-903-1103
 1-7/6-3/2-11/6-5/3
 otonal
 22
10
 0-401-702-903-1103
 1-7/6-10/7-11/6-5/3
 swetismic
 22
11
 0-201-502-702-1202
 1-9/7-11/7-10/7-9/8
 werckismic
 24
12
 0-301-502-702-1202
 1-11/9-11/7-10/7-9/8
 jove
 24
13
 0-201-502-903-1202
 1-9/7-11/7-11/6-9/8
 jove
 24
14
 0-301-502-903-1202
 1-11/9-11/7-11/6-9/8
 jove
 24
15
 0-201-602-903-1202
 1-9/7-3/2-11/6-9/8
 jove
 24
16
 0-301-602-903-1202
 1-11/9-3/2-11/6-9/8
 rastmic
 24
17
 0-201-702-903-1202
 1-9/7-10/7-11/6-9/8
 jove
 24
18
 0-301-702-903-1202
 1-11/9-10/7-11/6-9/8
 jove
 24
19
 0-502-702-903-1202
 1-11/7-10/7-11/6-9/8
 jove
 24
20
 0-301-502-1003-1202
 1-11/9-11/7-7/4-9/8
 jove
 24
21
 0-301-602-1003-1202
 1-11/9-3/2-7/4-9/8
 jove
 24
22
 0-301-702-1003-1202
 1-11/9-10/7-7/4-9/8
 jove
 24
23
 0-502-702-1003-1202
 1-11/7-10/7-7/4-9/8
 werckismic
 24
24
 0-301-502-903-1503
 1-11/9-11/7-11/6-11/8
 utonal
 30
25
 0-301-602-903-1503
 1-11/9-3/2-11/6-11/8
 rastmic
 30
26
 0-301-502-1003-1503
 1-11/9-11/7-7/4-11/8
 werckismic
 30
27
 0-301-602-1003-1503
 1-11/9-3/2-7/4-11/8
 jove
 30
28
 0-301-502-1202-1503
 1-11/9-11/7-9/8-11/8
 jove
 30
29
 0-301-602-1202-1503
 1-11/9-3/2-9/8-11/8
 rastmic
 30
30
 0-301-903-1202-1503
 1-11/9-11/6-9/8-11/8
 rastmic
 30
31
 0-502-903-1202-1503
 1-11/7-11/6-9/8-11/8
 jove
 30
32
 0-602-903-1202-1503
 1-3/2-11/6-9/8-11/8
 rastmic
 30
33
 0-301-1003-1202-1503
 1-11/9-7/4-9/8-11/8
 jove
 30
34
 0-502-1003-1202-1503
 1-11/7-7/4-9/8-11/8
 werckismic
 30
35
 0-602-1003-1202-1503
 1-3/2-7/4-9/8-11/8
 otonal
 30
36
 0-202-501-702-1703
 1-20/11-10/9-10/7-5/4
 utonal
 34
37
 0-501-702-1003-1703
 1-10/9-10/7-7/4-5/4
 werckismic
 34
38
 0-202-501-1103-1703
 1-20/11-10/9-5/3-5/4
 utonal
 34
39
 0-202-702-1103-1703
 1-20/11-10/7-5/3-5/4
 utonal
 34
40
 0-501-702-1103-1703
 1-10/9-10/7-5/3-5/4
 utonal
 34
41
 0-602-1003-1202-1703
 1-3/2-7/4-9/8-5/4
 otonal
 34
42
 0-702-1003-1202-1703
 1-10/7-7/4-9/8-5/4
 werckismic
 34
43
 0-602-1003-1503-1703
 1-3/2-7/4-11/8-5/4
 otonal
 34
44
 0-602-1202-1503-1703
 1-3/2-9/8-11/8-5/4
 otonal
 34
45
 0-1003-1202-1503-1703
 1-7/4-9/8-11/8-5/4
 otonal
 34

Hexads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-201-502-702-903-1202
 1-9/7-11/7-10/7-11/6-9/8
 jove
 24
2
 0-301-502-702-903-1202
 1-11/9-11/7-10/7-11/6-9/8
 jove
 24
3
 0-301-502-702-1003-1202
 1-11/9-11/7-10/7-7/4-9/8
 jove
 24
4
 0-301-502-903-1202-1503
 1-11/9-11/7-11/6-9/8-11/8
 jove
 30
5
 0-301-602-903-1202-1503
 1-11/9-3/2-11/6-9/8-11/8
 rastmic
 30
6
 0-301-502-1003-1202-1503
 1-11/9-11/7-7/4-9/8-11/8
 jove
 30
7
 0-301-602-1003-1202-1503
 1-11/9-3/2-7/4-9/8-11/8
 jove
 30
8
 0-202-501-702-1103-1703
 1-20/11-10/9-10/7-5/3-5/4
 utonal
 34
9
 0-602-1003-1202-1503-1703
 1-3/2-7/4-9/8-11/8-5/4
 otonal
 34